A/D and D/A conversion In this problem, A/D and D/A conversion are practiced and two simulations are compared. Consider the steps in Figure 2.11.

The quantizer is the three-bit uniform quantizer shown in Figure 2.4. The reproducer is a D/A converter. It converts the binary labels into analog values and holds the analog value until the next new binary label is available. h1(t) and h2(t) are both low-pass filters, where h1(t) is called the antialiasing filter. They are Butterworth filters with transfer functions H1ðsÞ ¼ H2ðsÞ ¼

1:984  1012 s3 þ 2:513  104s2 þ 3:158  108s þ 1:984  1012 :

The input is a triangle wave as depicted in Figure 2.12. T0¼1/f0¼1 ms. The sample rate is 20k samples/s. In the first experiment, compute the mean square error. Notice, the A/D converter has no information about the input phase. In the second experiment, the antialiasing filter h1(t) is removed. Compute the mean square error in this situation.